{
  "abstract": "We prove a nearly optimal lower bound on the blocklength of general relaxed locally decodable codes (RLDCs), extending the result of [GGS26] to nonlinear encodings and adaptive decoders with two-sided error. Namely, we show that any $q$-query RLDC $C\\colon \\{0,1\\}^k \\to \\{0,1\\}^n$ must satisfy $n = k^{1+Ω(1/q)}$, closely matching the upper bound of $n = k^{1+O(1/q)}$ by Ben-Sasson, Goldreich, Harsha, Sudan, and Vadhan (STOC 2004). Our proof reduces showing RLDC lower bounds to estimating the output distribution of adaptive decoders. To this end, we introduce a capped Horvitz--Thompson estimator with uniformly bounded discrete derivatives on the $p$-biased cube. We establish its concentration of measure via self-bounding inequalities and control the downward bias induced by capping through a spreadness argument.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.04678",
  "author_total": 3,
  "authors": [
    {
      "name": "Guy Goldberg"
    },
    {
      "name": "Tom Gur"
    },
    {
      "name": "Sidhant Saraogi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/04m3xe2ck0t9p.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.04678",
  "fulltext_url": null,
  "id": "04m3xe2ck0t9p",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.04678",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.CC"
    ],
    [
      "arxiv",
      "cs.IT"
    ],
    [
      "arxiv",
      "math.IT"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.04678",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/04m3xe2ck0t9p.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T15:21:29Z",
      "native_id": "2611.04678",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.04678"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.IT",
      "subfield": "general"
    }
  ],
  "title": "Lower Bounds for Adaptive Relaxed Locally Decodable Codes via the Capped Horvitz--Thompson Estimator",
  "title_text": "Lower Bounds for Adaptive Relaxed Locally Decodable Codes via the Capped Horvitz--Thompson Estimator",
  "type": "preprint",
  "updated_at": "2026-11-06T18:21:01Z",
  "url": "https://research.draconitic.com/paper/04m3xe2ck0t9p",
  "venue": "arXiv",
  "versions": []
}